A117375 -id:A117375 - cp's OEIS frontend

A117372 Riordan array (1-3x,x(1-x)).

1, -3, 1, 0, -4, 1, 0, 3, -5, 1, 0, 0, 7, -6, 1, 0, 0, -3, 12, -7, 1, 0, 0, 0, -10, 18, -8, 1, 0, 0, 0, 3, -22, 25, -9, 1, 0, 0, 0, 0, 13, -40, 33, -10, 1, 0, 0, 0, 0, -3, 35, -65, 42, -11, 1, 0, 0, 0, 0, 0, -16, 75, -98, 52, -12, 1

Offset: 0

Paul Barry, Mar 10 2006

Row sums are A117373. Diagonal sums are A117374. Inverse is A117375.

			Triangle begins
1,
-3, 1,
0, -4, 1,
0, 3, -5, 1,
0, 0, 7, -6, 1,
0, 0, -3, 12, -7, 1,
0, 0, 0, -10, 18, -8, 1,
0, 0, 0, 3, -22, 25, -9, 1

Number triangle T(n,k)=(-1)^(n-k)(C(k,n-k)+3*C(k, n-k-1))

A117376 Expansion of 1/((1-3xc(x))(1-x^2c(x))), c(x) the g.f. of A000108.

Original entry on oeis.org

1, 3, 13, 55, 240, 1057, 4688, 20879, 93250, 417272, 1869725, 8386137, 37640961, 169042436, 759470361, 3413223919, 15343588991, 68988110756, 310233741889, 1395268187372, 6275807975664, 28230370862051, 126996552221811

Offset: 0

Paul Barry, Mar 10 2006

Diagonal sums of number triangle A117375.

a(n)=sum{k=0..floor(n/2), [k<=n-k]*sum{j=0..n-k, (j/(n-k-j))*C(2n-k-j,n-k-j)[k<=j]*3^(j-k)}}

cp's OEIS Frontend

A117372 Riordan array (1-3x,x(1-x)).

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A117376 Expansion of 1/((1-3xc(x))(1-x^2c(x))), c(x) the g.f. of A000108.

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Author

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Comments

Formula

cp's OEIS Frontend

A117372 Riordan array (1-3x,x(1-x)).

Views

Author

Keywords

Comments

Examples

Formula

A117376 Expansion of 1/((1-3x*c(x))(1-x^2*c(x))), c(x) the g.f. of A000108.

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Author

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Comments

Formula

A117376 Expansion of 1/((1-3xc(x))(1-x^2c(x))), c(x) the g.f. of A000108.